Prove that: `sin^2 6x-sin^2 4x=sin2xsin10 x`

Explanation

To prove that \( \sin^2 6x - \sin^2 4x = \sin 2x \sin 10x \), we will start with the left-hand side and simplify it step by step.

### Step 1: Use the difference of squares formula
We can apply the difference of squares formula, which states that \( a^2 - b^2 = (a + b)(a - b) \).

\[ \sin^2 6x - \sin^2 4x = (\sin 6x + \sin 4x)(\sin 6x - \sin 4x) \]
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